Star-shaped Local Density of States around Vortices in a Type II Superconductor

The electronic structure of vortices in a type II superconductor is analyzed within the quasi-classical Eilenberger framework. The possible origin of a sixfold ``star'' shape of the local density of states, observed by scanning tunneling microscope experiments on NbSe$_2$, is examined in the light of the three effects; the anisotropic pairing, the vortex lattice, and the anisotropic density of states at the Fermi surface. Outstanding features of split parallel rays of this star are well explained in terms of an anisotropic $s$-wave pairing. This reveals a rich internal electronic structure associated with a vortex core.Comment: 4 pages, REVTeX, 3 figures available upon reques

SO(5) theory of insulating vortex cores in high-TcT_c materials

We study the fermionic states of the antiferromagnetically ordered vortex cores predicted to exist in the superconducting phase of the newly proposed SO(5) model of strongly correlated electrons. Our model calculation gives a natural explanation of the recent STM measurements on BSCCO, which in surprising contrast to YBCO revealed completely insulating vortex cores.Comment: 4 pages, 1 figur

Quasiparticle States at a d-Wave Vortex Core in High-Tc Superconductors: Induction of Local Spin Density Wave Order

The local density of states (LDOS) at one of the vortex lattice cores in a high Tc superconductor is studied by using a self-consistent mean field theory including interactions for both antiferromagnetism (AF) and d-wave superconductivity (DSC). The parameters are chosen in such a way that in an optimally doped sample the AF order is completely suppressed while DSC prevails. In the mixed state, we show that the local AF-like SDW order appears near the vortex core and acts as an effective local magnetic field on the quasiparticles. As a result, the LDOS at the core exhibits a double-peak structure near the Fermi level that is in good agreement with the STM observations on YBCO and BSCCO. The presence of local AF order near the votex core is also consistent with the recent neutron scattering experiment on LSCO.Comment: 4 pages, 2 ps figure

A Self-Consistent Microscopic Theory of Surface Superconductivity

The electronic structure of the superconducting surface sheath in a type-II superconductor in magnetic fields $H_{c2}<H<H_{c3}$ is calculated self-consistently using the Bogoliubov-de Gennes equations. We find that the pair potential $\Delta(x)$ exhibits pronounced Friedel oscillations near the surface, in marked contrast with the results of Ginzburg-Landau theory. The role of magnetic edge states is emphasized. The local density of states near the surface shows a significant depletion near the Fermi energy due to the development of local superconducting order. We suggest that this structure could be unveiled by scanning-tunneling microscopy studies performed near the edge of a superconducting sample.Comment: 12 pages, Revtex 3.0, 3 postscript figures appende

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc

Evaluation of Exchange-Correlation Energy, Potential, and Stress

We describe a method for calculating the exchange and correlation (XC) contributions to the total energy, effective potential, and stress tensor in the generalized gradient approximation. We avoid using the analytical expressions for the functional derivatives of E_xc*rho, which depend on discontinuous second-order derivatives of the electron density rho. Instead, we first approximate E_xc by its integral in a real space grid, and then we evaluate its partial derivatives with respect to the density at the grid points. This ensures the exact consistency between the calculated total energy, potential, and stress, and it avoids the need of second-order derivatives. We show a few applications of the method, which requires only the value of the (spin) electron density in a grid (possibly nonuniform) and returns a conventional (local) XC potential.Comment: 7 pages, 3 figure

The Current Carried by Bound States of a Superconducting Vortex

We investigate the spectrum of quasiparticle excitations in the core of isolated pancake vortices in clean layered superconductors. Analysis of the spectral current density shows that both the circular current around the vortex center as well as any transport current through the vortex core is carried by localized states bound to the core by Andreev scattering. Hence the physical properties of the core are governed in clean high-$\kappa$ superconductors (e.g. the cuprate superconductors) by the Andreev bound states, and not by normal electrons as it is the case for traditional (dirty) high-$\kappa$ superconductors.Comment: 17 pages in a RevTex (3.0) file plus 5 Figures in PostScript. Submitted to Physical Review

Ab initio Molecular Dynamics in Adaptive Coordinates

We present a new formulation of ab initio molecular dynamics which exploits the efficiency of plane waves in adaptive curvilinear coordinates, and thus provides an accurate treatment of first-row elements. The method is used to perform a molecular dynamics simulation of the CO_2 molecule, and allows to reproduce detailed features of its vibrational spectrum such as the splitting of the Raman sigma+_g mode caused by Fermi resonance. This new approach opens the way to highly accurate ab initio simulations of organic compounds.Comment: 11 pages, 3 PostScript figure

Local density of states in the vortex lattice in a type II superconductor

Local density of states (LDOS) in the triangular vortex lattice is investigated based on the quasi-classical Eilenberger theory. We consider the case of an isotropic s-wave superconductor with the material parameter appropriate to NbSe_2. At a weak magnetic field, the spatial variation of the LDOS shows cylindrical structure around a vortex core. On the other hand, at a high field where the core regions substantially overlap each other, the LDOS is sixfold star-shaped structure due to the vortex lattice effect. The orientation of the star coincides with the experimental data of the scanning tunneling microscopy. That is, the ray of the star extends toward the nearest-neighbor (next nearest-neighbor) vortex direction at higher (lower) energy.Comment: 10 pages, RevTex, 32 figure

Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations

We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead for performing the integrals that involves non-local parts of pseudopotentials, with keeping a high degree of accuracy. Our procedure gives rise to no Pulay forces, unlike other real-space methods using adaptive coordinates. Moreover, we demonstrate the potential power of the method by calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure